Spock is a lousy detective
hedetective he bet everything on finding the Gravity boots -- it never occurred to him it would turn out pointless if, as happened, they were unable to link the boots to the murderers.
the only thing that saved their... Bacon was what they hadn't considered-- that there were also some blood-stained uniforms.
"After years of fighting with reality, I am pleased to say that I have finally won out over it."